FR H-Volatility - page 31
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Well, that's more an indication that it's not Wiener, but I'd be wary of saying it's not accidental, grasn. Or are you talking about independence?
Not technically a Wiener. I added some emotion and got a non-random one. :o)
to Neutron.
Seryoga hello. Explain, please, where did you get this from:
I am interested in the formula y=+-m*SQRT(t) itself, how did you get it, where did you get it from?
Hi Sergey!
This statement is true for the process of one dimensional Brownian motion, trajectory of which is described by consecutive accumulation of random, normally distributed increments with zero expectation. For the first time, Albert Einstein, in my opinion, at the end of the 19th century got an analytic expression relating the mean square of the particle's trajectory deviation from the starting point and the time, when he gave the complete model of a suspended particle motion under the action of random forces (collisions with molecules).
Of course, price increments can only be considered random in first approximation, but as an estimate it is good enough. Hence the formula and the statement that the process of pricing resembles diffusion in one-dimensional space (by analogy with physics).
Well, the formulas you cite are probably marginal estimates given the presence of "fat tails"... for example.
Hi Sergey!
This statement is true for a one dimensional Brownian motion process, the trajectory of which is described by sequential accumulation of random, normally distributed increments with zero expectation. For the first time, Albert Einstein, in my opinion, at the end of the 19th century got an analytic expression relating the mean square of the particle's trajectory deviation from the starting point and the time, when he gave the complete model of a suspended particle motion under the action of random forces (collisions with molecules).
Of course, price increments can only be considered random in first approximation, but as an estimate it is good enough. Hence the formula and the statement that the process of price formation resembles diffusion in one-dimensional space (by analogy with physics).
Well, the formulas you cite are probably marginal estimates given the presence of "fat tails"... for example.
Well, the formulas you gave are probably marginal estimates, taking into account the presence of "fat tails"... for example.
I'll show you the result when I make the equivolume bar hook, maybe something interesting will come out. It is not as simple as it seemed at the beginning...
What might be the thick tails in a Wiener process (or rather, in its increments)?
You're probably right!
Mathemat, take a look at this:
The figure shows EUR/GBP minutes (red) and the sum of equal price increments (delta=co) with direction retention (blue). Notice how they behave differently! I thought that for forecasting of prices it is enough to have an adequate model that predicts the expected direction of price movement, because the amplitude is not a problem! - It is equal to the volatility, that's all. However, this turned out to be a delusion. The direction of the price drift depends not so much on the prevalence of one or another direction, as on the balance between the long-short volatility!
Note that the series of equal increments (series of first differences) is stationary because MO=0, sko=const, and therefore you can work with it using the available potential for BP analysis. Next, we have two series of increments or volatility (short and long) of initial BP. As we know that volatility is persistent, and, therefore, we can apply a standard set of indicators to its analysis, for example a moving average (in this case it must work). It turns out that we:
1. we have decomposed the initial BP on some basis;
2. each of the elements of decomposition is predictable by standard methods;
3. The initial series is completely reconstructed from the elements of the expansion with the possibility of forecasting!
Such is the hypothesis. What do you think about it?
Well, the formulas you gave are probably marginal estimates, taking into account the presence of "fat tails"... for example.
I'll show you the result when I make the equivolume bar hook, maybe something interesting will come out. It is not as simple as it seemed at the beginning...
That's right, I wrote so honestly - for a Wiener process, aka Brownian motion. The source is the fundamental work "Theory of Random Processes" written by Shiryaev. There is a whole interesting section "Properties of trajectories of Brownian motion", or so it is called, I do not remember exactly. And the heavy tails of the Wiener process simply don't exist.
Neutron, do the ticks behave the same way - or are they no longer so unbridled? The only obvious explanation for the discrepancy here is that the minutes that are down are much longer than those that are up. And in general the result is very curious, clean...
See fig. red for cotier, blue for equal increments (EW) with the amplitude equal to the root of the cotier increments.
Interesting divergence of tick history from the real account opened at Alpari and data from their own history-center...
If we compare the "volatility" of RP for different timeframes and ticks, then the most "stationary" process is obtained on ticks. It is interesting - the collapse of the yen which happened in late July - early August, had almost no effect on the dynamics of the FP series - there was no catastrophe for it! It turns out that the crisis was not caused by the crowd, but by a few targeted, strong exchange rate movements.
See fig. red for cotier, blue for equal increments (EW) with the amplitude equal to the root of the cotier increments.
The formula by which the blue curve was generated can be used. With comments on each component, how and what was generated. Thank you. Or just a file, I can figure it out myself, I think I know Matcad.
If we compare the "looseness" of RPs for different timeframes and ticks, then the most "stationary" process is obtained on ticks. It is interesting, - the collapse of the Yen which happened in late July - early August, practically did not reflect on the dynamics of some RP - there was no catastrophe for it! It turns out that the crisis was not caused by the crowd, but by a few targeted, strong exchange rate movements.